EP 0 594 699 B1 discloses a machine tool for laser machining of workpieces that has a gantry arranged above a workpiece and a tool carrier arranged on the gantry. To generate a main movement of a laser beam arranged as a machining device on the tool carrier, the gantry is moved together with the tool carrier and/or the tool carrier is moved along the gantry. An auxiliary movement of the laser beam relative to the tool carrier is generated by means of a high-dynamic auxiliary device. In order to achieve an overall acceleration of the laser beam which is as high as possible, the movement of the gantry and the tool carrier is superimposed by the auxiliary laser-beam movement generated by means of the high-dynamic auxiliary device. In the case of this auxiliary movement, the laser beam starts from an invariable initial position.